$f$-Racks, $f$-Quandles, their Extensions and Cohomology

Indu R. U. Churchill; M. Elhamdadi; M. Green; A. Makhlouf

doi:10.1142/S0219498817502152

$f$-Racks, $f$-Quandles, their Extensions and Cohomology

Rings and Algebras 2016-11-30 v2 Algebraic Topology Quantum Algebra

Authors: Indu R. U. Churchill , M. Elhamdadi , M. Green , A. Makhlouf

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Abstract

The purpose of this paper is to introduce and study the notions of $f$ -rack and $f$ -quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order $f$ -quandles. Moreover, we define modules over $f$ -racks, discuss extensions and define a cohomology complex for $f$ -quandles.

Keywords

f-rack f-quandle extensions cohomology algebraic structures equational identities modules

Cite

@article{arxiv.1606.00353,
  title  = {$f$-Racks, $f$-Quandles, their Extensions and Cohomology},
  author = {Indu R. U. Churchill and M. Elhamdadi and M. Green and A. Makhlouf},
  journal= {arXiv preprint arXiv:1606.00353},
  year   = {2016}
}

Comments

We have changed the title, added couple of examples and corrected some typos. To be appeared in Journal of Algebra and its Applications

$f$-Racks, $f$-Quandles, their Extensions and Cohomology

Abstract

Keywords

Cite

Comments

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